Search and Prices in the Medigap Insurance Market

Search and Prices in the Medigap Insurance Market∗ Haizhen Lin† Matthijs R. Wildenbeest‡ September 2015

Abstract This paper studies search and prices in the Medigap insurance market. Using data on market shares, insurer characteristics, and plan prices, we estimate to what extent prices can be explained by search and product differentiation. In our model, consumers search across Medigap insurers for prices as well as plan types. Our estimates indicate search costs are substantial: the estimated median cost of searching for an insurer is $30. Using the estimated parameters we find that eliminating search costs could result in price decreases of as much as $63 (or 3.7 percent), along with increases in average consumer welfare of up to $236. Keywords: Medigap, health insurance, search, product differentiation, price dispersion JEL Classification: I13, D83, L15

∗ We thank Mike Baye, Kate Bundorf, Andrew Ching, Leemore Dafny, David Dranove, Hanming Fang, Marty Gaynor, Lorens Helmchen, Claudio Lucarelli, Nicole Maestas, Jeff Prince, Jon Skinner, Kosali Simon, Alan Sorensen, and conference participants at the 10th Annual International Industrial Organization Conference (IIOC) and 2012 American Society of Health Economists Conference (ASHEcon) for helpful comments and suggestions. † Indiana University, Kelley School of Business and NBER, E-mail: [email protected]. ‡ Indiana University, Kelley School of Business, E-mail: [email protected] (corresponding author).

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1

Introduction

Medigap is a form of private insurance designed to supplement Medicare by filling in the coverage gaps in Medicare payment. Medigap has a large share of the market for Medicare supplemental coverage; in 2009 Medigap provided coverage for about 20 percent of Medicare beneficiaries. One important feature of the Medigap market is plan standardization: as a result of the passage of the Omnibus Budget Reconciliation Act (OBRA) in 1990, all plans sold after July 1992 are required to conform to a set of standardized plans. This means that even though a plan type is usually offered by different insurers, it can be considered a homogenous good in terms of coverage. In addition to plan standardization, during a six-month open enrollment period that starts from the day an individual turns 65 and enrolls in Medicare Part B, insurers cannot decline a Medigap application because of pre-existing medical conditions. Due to this guaranteed issue, most beneficiaries enroll in a Medigap plan during open enrollment to avoid medical underwriting later on. Even though Medigap plans are standardized and selection is limited due to guaranteed issue, there is substantial price variation across insurers within states. For instance, a 65-year-old woman living in Indiana could expect to pay anywhere between $1,223 and $3,670 for a Medigap Plan F policy in 2009, depending on her choice of insurer. Such a wide range of prices is not limited to this state only: the average coefficient of variation within states is 0.27 for Plan F, which is substantial. Why are prices so dispersed for what is essentially a homogenous good? Since Stigler’s (1961) seminal article on the economics of information, economists have tried to answer this question by relating price dispersion to search frictions: if it is costly for individuals to obtain price information, because, for instance, finding out the price means visiting the seller or making phone calls, some individuals will not compare offers, which allows firms to raise prices. As a result firms might set high prices to maximize profits from individuals who do not compare offers, or set a relatively low price and maximize surplus from price comparers, resulting in price dispersion. An additional explanation for the observed price variation is that even though a specific Medigap plan is essentially a homogeneous goods, insurers might still differ in terms of quality or servicerelated characteristics, such as branding and billing services, allowing higher-quality insurers to set higher premiums. Product differentiation and search can also go together: as shown by Wolinsky (1986) and Anderson and Renault (1999), if consumers are searching not only for low prices, but also for horizontal characteristics such as the best-fitting plan type, equilibrium prices rise with search costs. In Section 3 of the paper we provide preliminary evidence that both firm-level product differ-

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entiation and search play important roles in the market for Medigap plans. We then use this as a motivation for developing a search and product differentiation model in Section 4. More specifically, we model search for plans that are both horizontally and vertically differentiated. Consumers determine before they search which of the insurers to contact for information about plans and prices; they do so by making a trade-off between the expected utility of contacting a subset of insurers and corresponding search costs.1 We show how to estimate the model using aggregate data on prices, market shares, and plan characteristics. An attractive feature of the model is that search costs are non-parametrically identified, i.e., we do not have to make any specific assumptions about the distribution of search costs among individuals. Although this means that we have to assume individuals are homogeneous in how they value observed characteristics (i.e., we cannot allow for random coefficients), it does allow us to separately identify search cost and preference heterogeneity without using additional data on search behavior, which is usually not available to researchers.2 We present our estimation results in Section 5. Our estimates indicate that search costs are substantial; the estimated parameters of our main specification indicate that median search costs are $30 per search. In addition there is a lot of variation in search costs across individuals. We also show how to use our estimates to study the competitive effects of lowering search costs. Assuming insurers set prices to maximize profits, we determine to what extent prices would change if quotes are obtained at no cost. According to our simulation results average prices decrease by $63, which is 3.7 percent of the average yearly policy premium. Consumer welfare, which also includes savings on search costs as well as the expansion of the market, increases by up to $236 on average if search costs are zero. We conclude in Section 6 by highlighting our main contributions, and by discussing some of the limitations of our model. Specifically, an important contribution of our paper is to provide a methodology that enables us to non-parametrically estimate search costs for differentiated goods when using aggregate data on demand. Even though we focus on the the market for Medigap plans, our model is general enough to be applied to other markets in which both search frictions and product differentiation are deemed important. 1

We believe that given the nature of the search process it is more natural to model search as first deciding on which insurers to search for, and then deciding which plan to subscribe to. For instance, to get more information consumers typically have to contact an insurer, which means that search costs tend to occur at the insurer level and to a lesser extent at the plan level (making a single phone call would allow consumers to obtain information on all plans sold by the insurer). 2 We will show later in the paper that allowing for random coefficients does not seem critical in this market.

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Related Literature Our paper is part of the literature that studies Medigap prices and price dispersion.3 Robst (2006) adopts a hedonic pricing model in order to examine the determinants of Medigap premiums. Our paper is closely related to Maestas, Schroeder, and Goldman (2009), who use the search model of Carlson and McAfee (1983) to model price dispersion for Medigap plans. They find that the average search cost in this market is $72. Although we find median search costs to be somewhat lower than this number, unlike Maestas, Schroeder, and Goldman (2009) we model the joint decision of which plan type to obtain and which insurer to choose. To allow for differences in plan-type preferences across individuals our utility specification includes a stochastic utility shock, which we model as exante unobserved by the decision maker. This means that in our model consumers search for prices as well as a good fit in terms of insurer and plan type. A second difference between our model and that of Maestas, Schroeder, and Goldman (2009) is that search in their model is random, while search in our model is directed, which means that individuals rank insurers according to expected utility, and, depending on the decision-maker’s search costs, contact an optimal set of the highestranked insurers to obtain information about prices and plan-type matches. In differentiated product markets in which consumers have some prior information on the characteristics of the firms, the optimal way to search is to start with the alternative that provides the highest expected utility (see, for instance, Weitzman, 1979; Chade and Smith, 2006). In Maestas, Schroeder, and Goldman (2009) consumers have no prior information on the parameters of the utility function, which means ex-ante all alternatives are similar and consumers search randomly.4 In a random search model lower ranked firms are as likely to be part of a consumer’s choice set as higher ranked firms, whereas in our directed search model a consumer needs to have low search costs to sample a lower ranked firm. To explain demand at lower ranked firms search costs therefore have to be lower in our search model than in the random search model, which means that search cost estimates will likely be higher in a random search model. Finally, whereas Maestas, Schroeder, and Goldman (2009) assume that search costs are uniformly distributed, our model does not require us to make any assumptions on the shape of the search cost distribution, which can be an advantage if one does 3 The earlier literature on Medigap has focused mostly on adverse selection (e.g., Wolfe and Goddeeris, 1991; Hurd and McGarry, 1997; Ettner, 1997; Finkelstein, 2004). A recent study by Starc (2014) finds that adverse selection can actually lower markups and thus increase consumer welfare. Fang, Keane, and Silverman (2008) instead find evidence of advantageous selection in Medigap and they identify various sources of advantageous selection such as income and cognitive ability. 4 Especially at the state level, the Medigap market is dominated by a few insurers with large market shares, which is difficult to explain if product differentiation would not be playing a role. Medigap insurers tend to be active in other markets as well and spend significant amounts on advertising. This in combination with word of mouth effects makes it likely that consumer have some prior knowledge of at least some of the characteristics of the firms.

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not know a priori how the search cost distribution looks like. Moreover, search costs are typically interpreted as being related to income—since the income distribution tends to follow a lognormal distribution, assuming search costs follow a uniform distribution may be restrictive. Our paper also adds to the consumer search literature. Brown and Goolsbee (2002) show that increased usage of Internet price comparison sites reduced search costs and thereby led to lower prices for term life policies. Horta¸csu and Syverson (2004) develop a model of product differentiation and search and find that both are important determinants of fee dispersion in the retail S&P 500 index funds sector. Cebul et al. (2011) find that search frictions in private health insurance markets lead to high prices and price dispersion, excessive marketing costs, and high insurance turnover. They also suggest that government-financed public insurance can reduce distortions created by search frictions. Wildenbeest (2011) provides a framework for studying price dispersion in markets with product differentiation and search frictions and shows how to estimate search costs using only price data. Our paper most closely relates to a study by Moraga-Gonz´alez, S´andor, and Wildenbeest (2015), who add search to the demand estimation framework of Berry, Levinsohn, and Pakes (1995). Moraga-Gonz´ alez, S´ andor, and Wildenbeest (2015) estimate the model using automobile data from the Netherlands. To be able to separately identify heterogeneity in search costs from heterogeneity in preference parameters, they link search costs to the distances between consumers and dealer locations. Our model builds on their findings; however, by working in a conditional logit rather than a mixed logit framework, search costs can be non-parametrically identified, which is useful if the data lack a suitable search cost shifter, as in our data.

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Industry

Medigap, or Medicare supplemental health insurance, is a form of private insurance designed to supplement Medicare by filling in the coverage gaps in Medicare payment. Since its inception in 1965, Medicare, a federal health insurance program for the elderly, has been the primary form of health insurance for a majority of seniors in the United States.5 Basic Medicare has substantial cost-sharing and gaps in coverage, and does not include an upper limit on beneficiaries’ out-ofpocket spending. In 2009, for example, Medicare Part A (inpatient insurance) required an enrollee to pay a total deductible of $1,068 for the first 60 days of a hospital stay, $267 per day for days 5

Medicare includes two basic parts: Part A, inpatient insurance, and Part B, outpatient insurance. Enrollment in Part A starts automatically for the eligible when they turn 65; no premium is involved. To be eligible for Medicare, an individual or his or her spouse must pay Medicare taxes for at least 10 years. If this criterion is not met, individuals can purchase Part A by paying a monthly premium, which was up to $443 per month in 2009. Part B enrollment requires a monthly premium (the base rate, which increases if an individual’s yearly income exceeds $85,000, was $94.60 in 2009); almost all elderly individuals choose to enroll.

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61-90, $534 per day for days 91-150, and all costs for each day beyond 150 days. Under Medicare Part B (outpatient insurance), enrollees were responsible for a total deductible of $135 in 2009 as well as a 20 percent coinsurance payment of the Medicare-approved amount for covered services after the deductible had been reached. Since basic Medicare leaves the elderly at a substantial financial risk, in 2009 over 90 percent of beneficiaries had some kind of supplemental insurance to fill in the coverage gaps in basic Medicare. Of the different sources of supplemental insurance, Medigap provided coverage for about 20 percent of the Medicare beneficiaries in 2009 (Sheingold, Shartzer, and Ly, 2011).6,7 The Medigap market is highly concentrated.8 United Health Group has the largest national market share of about 31 percent. The Mutual of Omaha Group has a market share of more than 8 percent. Another five firms have over two percent of the market: Wellpoint Inc Group (6.4 percent), Health Care Services Group (5.0 percent), CNO Financial Group (3.6 percent), BCBS of Michigan Group (2.2 percent), and Highmark Group (2.1 percent). The remaining 42 percent consists of firms that have less than two percent of the market each. One important feature of the Medigap market is plan standardization. With the passage of the Omnibus Budget Reconciliation Act (OBRA) in 1990, all new policies sold after July 1992 are required to conform to a set of standardized plans (Massachusetts, Minnesota, and Wisconsin are not subject to the standardization). Each plan must offer the standard set of benefits regardless of which company sells it. Plan standardization was intended to promote competition among insurers and to avoid misunderstanding and confusion among seniors regarding coverage. Over time, the set of standardized plans has been modified. For example, Plans K and L were introduced in June 2006 following the Medicare Prescription Drug, Modernization, and Improvement Act of 2003. As of 2009, a total of twelve standardized plans, labeled by the letters A through L, were offered.9 Of these twelve plans, Plan A is considered the basic plan, covering Medicare Part A hospital 6

Another 30 percent had supplemental coverage through an employer-sponsored plan, and over 25 percent were enrolled in Medicare Advantage plans that provide additional benefits on top of traditional Medicare. In addition, about 15 percent of beneficiaries were covered by Medicaid due to dual eligibility, and about 1 percent were covered by other plans such as VA plans. The remaining 9 percent had no supplemental coverage. 7 The distribution across different types of supplemental coverage was relatively stable between 2001 and 2005. Since 2006, however, there has been a decline in Medigap coverage. For example, the percentage of Medicare beneficiaries covered by Medigap dropped from slightly less than 25 percent in 2001 to about 20 percent in 2009 and 2010. The decline in Medigap enrollment has coincided with a steady increase in Medicare Advantage enrollment. As a result, the combination of these two types of coverage increased slightly from less than 40 percent in 2005 to almost 45 percent in 2009. 8 The following statistics on market shares are based on our calculations using the 2009 National Association of Insurance Commissioners’Medigap Experience Files. To provide an overall view of market concentration, we use data on the number of current polices (as of December 31, 2009), including both individual plans and group plans through employers. Note that for the estimation of our model, we only consider individual plans as this paper focuses on consumer search frictions in the market for individual coverage. 9 Plans M and N were first offered in June 2010 and will not be studied in this paper.

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stay coinsurance for days 61 to 150 and all Medicare Part B coinsurance payments. All other plans include additional coverage options.10 Not all plans are available in each state. Insurers that operate in a given state are required to offer at least the basic plan (Plan A). If they choose to offer other plans, Plan C or F has to be provided too. So far Plan F, which offers the second-most comprehensive coverage, has been the most popular plan type, enrolling more than 40 percent of Medigap policy holders. Another important feature of the Medigap market is that during open enrollment insurers cannot deny coverage to an eligible applicant because of health status (guaranteed issue).11 The OBRA 1990 mandates a six-month open enrollment period for Medigap, starting from the day an individual turns 65 and enrolls in Medicare Part B. During the open enrollment period, insurers cannot decline an individual’s application or charge a higher premium because of an applicant’s pre-existing medical conditions. Medical underwriting is allowed after the open enrollment period, making it difficult to switch to a new plan. As a result, the majority of seniors subscribes to a Medigap plan during the open enrollment period in which medical underwriting is prohibited. In addition to plan standardization and the absence of medical underwriting during the openenrollment period, Medigap premiums are subject to regulation.12 Premiums are allowed to vary on the basis of age, gender, and smoking status. Regarding age, three different rating methods can be used: attained-age, issue-age, and community-rated. Attained-age means that premiums are allowed to increase with the age of the policy holder. Issue-age premiums are charged based on the age when the policy holder enrolls. Under issue-age rating, premiums are only allowed to increase to compensate for rising healthcare costs over time, and premium increases cannot be based on the age of the policy holder. Community-rating premiums are uniform across all subscribed individuals in the community.13 At the entry age of 65, premiums are higher for issue-age plans in comparison to attained-age plans in order to incorporate increases in utilization as individuals age (Robst, 2006). Premium differences based on gender are minimal, and premiums for smokers are on average higher than for non-smokers. 10

Some plans have altered their amount of coverage over time. For instance, before the introduction of the Medicare Part D program in 2006, Plans H to J also offered limited outpatient prescription drug coverage. 11 When a beneficiary’s current source of coverage is no longer available, insurers operating in the market are required to offer a policy regardless of health status. For more details on this see the official Medigap guide published by CMS, “Choosing a Medigap Policy: A Guide to Health Insurance for People with Medicare.” 12 State departments of insurance or other state agencies have the authority to approve insurance policy forms and premiums (Sheingold, Shartzer, and Ly, 2011). A state’s regulation is required to meet the National Association of Insurance Commissioners Model Standards. In addition, all insurers are subject to regulations on a minimum loss ratio of 65 percent for individual policies, which means that plans must spend at least 65 dollars on medical care for every 100 dollars in premium. 13 Several states, including Connecticut, New York, and Vermont, mandate community rating.

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Regardless of plan standardization, we observe large price variation in Medigap plans within a market, even after controlling for factors such as plan type, age, gender, smoking status, and rating method. In the remainder of this paper we study how prices and price dispersion in otherwise homogenous Medigap plans are related to product differentiation and consumer search frictions.

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Data and Basic Analysis

3.1

Data

Our data come from two sources. Data on premiums come from Weiss Ratings, which provide detailed pricing information for Medigap plans offered in 2009. The data include information on insurers, location, plan type, gender, age group, and some other characteristics such as rating method (attained-age, issue-age, and community-rated) and smoking status. Data on market shares are derived from the National Association of Insurance Commissioners’ (NAIC) Medigap Experience Files. The NAIC dataset provides information on the number of active policies as of December 31, 2009, as well as other variables such as total premiums and claim volumes for 2009. This dataset allows us to differentiate between individual plans and group plans that are sold through employers. Since we are interested in how individual consumers make purchase decisions, our focus is on individual plans. The number of policies issued before 2007 and from 2007 to 2009 combined are reported separately.14 Policies issued before 2007 represent policy holders who subscribed before 2007 and chose to renew their policies up to 2009. For the calculations of the market shares used in our empirical analysis, we only use policies newly issued between 2007 and 2009.15 One obvious advantage of this measure is that we can focus our analysis on new policies sold to individuals who turned 65 and became eligible to purchase a Medigap plan. Market shares are constructed in a similar way in Starc (2014) and Fang, Keane, and Silverman (2008). Several steps were taken before we merged the two datasets. We first dropped observations from the three states (Massachusetts, Minnesota, and Wisconsin) that are exempt from federal 14 According to the data reporting instructions, the NAIC dataset provides a snapshot of the number of individuals covered under each policy on December 31 of each year reported. This means that we can only infer from the data the net gain in the number of covered lives. For example, suppose an insurer shows 10 covered lives for the most current three years (2007-2009). If a member bought a policy in April 2009 and passed away in November 2009, the person would not be reflected in the year-end covered lives number. The actual number of policies sold for the year is 11, but because of the way in which the data is captured, we do not observe the policy sold to the deceased policy holder. 15 Ideally, we would like to observe new policies sold only in 2009 to match our pricing data. However, only three years of combined data are available through NAIC, which, to the best of our knowledge, is the most comprehensive source of Medigap market share information.

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regulation and offer a different set of plans. Second, we dropped select plans (less than 1 percent of the market share)16 from both data sources and tobacco plans from the pricing data.17 In a third step we calculated insurer-specific aggregated state-level premiums by taking insurers’ average prices for a given plan over all zip codes within a state, which allows us to match the price data to the state-level market share data.18 Although this means loss of some price variation, most insurers offer the same plan type at only a limited number of prices across different areas within a state: more than 40 percent of plans are offered at a single price; for about 30 percent of plans the insurer has set two different prices within a state; and over 90 percent of plans are offered at fewer than three different prices.19 This lack of regional price variation has been documented in previous studies as well (see, for instance, Maestas, Schroeder, and Goldman, 2009) and might be explained by the fact that the premiums charged by an insurer need approval from state insurance offices. The merged dataset contains information on prices and sales for each Medigap policy offered by each insurer at the state level. It corresponds to a total of 4,704 observations (at the state-insurerplan level), accounting for more than 80 percent of the total policies sold between 2007 and 2009. A total of 109 companies are observed in the data, of which 14 operate in more than 30 states. The median number of states in which an insurer operates is 6. Note that the NAIC data only reports covered lives for all ages combined. Since most new policies were sold to individuals at the open enrollment period, and since most premiums do not differ across gender, the prices we use for estimating the model are the premiums for 65-year-old females (following Maestas, Schroeder, and Goldman, 2009).20 16 Medigap select plans have lower premiums in comparison to standard plans but offer a limited provider network. We focus on non-select plans for several reasons. Firstly, select plans are not common. In our data, less than 5 percent of plans are select plans (this has also been noted in a study by Fox, Snyder, and Rice, 2003). Secondly, it would be difficult to control for plan characteristics for select plans, as each select plan might have a network that is unobserved by us. 17 The NAIC data does not report covered lives separately for smokers and non-smokers. We use the non-smoking rate, as the vast majority of the elderly are non-smokers (according to data from the Centers for Disease Control and Prevention, about 90 percent of the elderly do not smoke). 18 Premiums also vary by rating method, whereas our sales data does not differentiate according to rating method. Nevertheless, we find that more than 93 percent of firms use only one rating method for all plans in a given state. Moreover, around 98 percent of observations (at the state-insurer-plan level) are offered at one rating method only, which means that for these observations our premium data match our sales data quite well. For the remaining 2 percent of observations, we choose the rating method with the highest frequency in the data as the relevant rating method. 19 The average coefficient of variation of premiums set by the same insurer for a given plan type across zip codes within a state is 0.03, with the 75th percentile equal to 0.07. 20 For those observations that reveal a difference between male and female premiums, the mean difference is only around 7 percent of the average price (with a 99th percentile of approximately 19 percent).

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3.2

Price Dispersion and Cost Heterogeneity

Price dispersion There exists large price variation for Medigap plans across insurers within a state. Take premiums for Medigap Plan F (the most popular plan) in Indiana as an example: a total of 40 companies offered Plan F in Indiana in 2009, and premiums for a 65-year-old woman using the attained-age rating method (the most popular rating method) range from $1,223 to $3,670, with a median of $1,818. To get a better picture of the extent of premium variation, Table 1 summarizes the coefficient of variation by rating method, averaged over plan types and states.21 For all three rating methods the coefficient of variation is substantial. Attained-age and issue-age show slightly higher variation than a community-based rating. Moreover, there is substantial variation in the coefficient of variation across plan types and states; whereas in a few states some plan types show hardly any price variation, the coefficient of variation can be as high as 0.65 for the issue-age rating method. Note that Table 1 is calculated using prices for 65 year old females only; as reported above, prices for different age groups as well as for males follow similar patterns. Table 1: Coefficient of Variation Rating

Mean

S.D.

Min

5%

25%

Attained-Age Issue-Age Community

0.217 0.215 0.208

0.082 0.122 0.114

0.000 0.002 0.009

0.071 0.043 0.018

0.173 0.118 0.154

Percentiles 50% 75% 0.216 0.201 0.197

0.267 0.290 0.263

95%

Max

0.344 0.450 0.381

0.486 0.651 0.559

Notes: All reported values are averaged over plan types and states.

Table 2 reports average prices and coefficient of variation by plan type for the attained-age rating plans, the most popular rating method in the data. The average price varies greatly across states. For example, the average premium for plan A is $1,128 across states, with a standard deviation of 152. Also the average difference between the minimum and maximum premium charged within a state is substantial. For instance, for Plan A the average difference is $869, which is close to 80 percent of Plan A’s mean price. Table 2 also shows that most plan types have an average coefficient of variation that exceeds 0.20. Plan F, the most popular and the second-most comprehensive plan, has the highest average price variation as measured by the coefficient of variation. 21

Since insurers use different rating methods for a given plan type within a state, we combine plan type and rating method to identify a product. This means that Plan F attained-age and Plan F issue-age are treated as different products.

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Table 2: Coefficient of Variation by plan type (attained-age) Plan Type

Price Mean S.D.

Max-Min Mean S.D.

Coefficient of Variation Mean S.D. Min Max

A B C D E F G H I J K L

1,128 1,567 1,804 1,437 1,509 1,813 1,422 1,468 1,515 1,746 1,030 1,455

869 959 1,490 927 535 1,889 868 278 319 721 215 322

0.241 0.247 0.255 0.203 0.225 0.261 0.205 0.111 0.187 0.170 0.223 0.229

152 261 190 199 284 194 197 217 210 181 161 265

488 512 594 482 446 760 437 226 359 353 204 334

0.087 0.078 0.052 0.061 0.111 0.040 0.046 0.047 0.104 0.055 0.078 0.118

0.000 0.081 0.160 0.009 0.014 0.194 0.085 0.031 0.044 0.055 0.041 0.004

0.415 0.486 0.370 0.278 0.478 0.341 0.323 0.226 0.483 0.341 0.377 0.430

Part of the variation in premiums across insurers might be attributed to plans that attract very few individuals due to high prices. To correct for differences in market share, we also calculated the coefficient of variation weighted by market share for each plan. The weighted coefficient of variation for Plan F under attained age rating averages 0.20 for 65-year-old females, indicating that considerable price dispersion among Medigap plans still remains even after controlling for differences in market share. Cost heterogeneity One plausible explanation for price variation in Medigap plans involves what is known as “endogenous sorting.” That is, insurers might have a different pool of risk types, with high-priced insurers attracting consumers that are more costly to insure. Though a majority of beneficiaries purchase Medigap during the open enrollment period when insurers cannot decline an application, firms might still target different types of consumers through marketing or advertising. In this case, consumers with different risk types then sort themselves into different insurers, and the equilibrium might be such that high-risk consumers select an insurer that charges a high premium while low-risk ones select an insurer that offers a low premium. To investigate whether and to what extent price variation across insurers can be explained by cost differentials, we use data on the total amount of claims filed for each observation (at the stateinsurer-plan level).22 We use the average claim, defined as the ratio of total claims to the total 22 Note that according to federal regulation, the loss ratio (defined as total claims divided by total premiums) cannot be lower than 65 percent for individual Medigap plans. If this minimum ratio is violated, an insurer is required to provide transfers to its policyholders to be compliant with the regulation. We observe large differences in loss ratio across plans. The average loss ratio is 0.80, but almost 40 percent of the insurer-plan combinations have

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number of covered lives, as a measure of the risk type for an average policyholder of a given plan, assuming a larger average claim indicates a higher risk type. We then run a regression of premiums on the average claim, after controlling for state-fixed effects, dummies for plan types, and dummies for rating methods, and we compare the results to a regression without controlling for the average claim. Table 3: Price Dispersion, Cost Differentials, and Firm Heterogeneity (1)

(2)

Average claims

Number of observations Insurer fixed effects R-squared

Premiums (3)

0.052 (0.003)∗∗∗ 4,704 No 0.394

4,686 No 0.425

(4) 0.026 (0.003)∗∗∗

4,704 Yes 0.677

4,686 Yes 0.684

The results are presented in columns 1 and 2 of Table 3. Column 1 is based on a regression without controlling for the average claim. Column 2 adds the average claim. We find that a onedollar increase in average claim is associated with a 5-cent increase in premium. The R-squared increases by about 3 percentage points, indicating that adding controls for the average claim does not contribute much to explaining the observed variation in premiums. Although not reported, we also run regressions separately for each plan type and find similar results. These results indicate that cost differentials are related to Medigap plan pricing but they do not play a major role in explaining the observed price variation across different insurers.

3.3

Product Differentiation and Search

As documented above, there is substantial price variation in Medigap plans, even though conditional on plan-type Medigap plans are homogeneous in terms of coverage. We also show that cost heterogeneity does not seem to help much to explain the observed price variation. In this subsection we provide evidence for two important determinants of this price variation, which we use to motivate the theoretical model we present in Section 4. a loss ratio below 65 percent.

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Product differentiation One explanation for the observed price variation is product differentiation. Although Medigap plans are standardized, premiums might still differ across insurers due to differences in other dimensions than plan characteristics. For example, a consumer might favor an older and more established firm or a firm with a better financial rating. Firms do differ in these attributes: age of the insurers ranges from 3 to 159 years and according to financial safety ratings provided by Weiss Ratings, 22 out of the 109 insurers in our dataset had a financial rating of A, 47 had a rating of B, and 12 were either unrated or rated below C.23 Firms also differ in the number of plans that are offered, as well as in how many states they are active. Other attributes one might expect to play a similar role are billing services, reputation, and brand name. Unfortunately we do not observe firm attributes other than age, safety rating, number of plans offered, and the number of states in which the firm is active. Still, pricing patterns may provide indirect evidence of whether firm-level product differentiation plays an important role in explaining price variation for Medigap plans. If price variation is solely caused by firm-type product differentiation, one would expect insurers to charge consistently high or low prices for all offered plans in a given state: if a better financial rating or reputation allows the insurer to charge a higher premium this is likely to happen for all plan types the firm is selling. To see if this is indeed the case in our data, for each plan type we compare each insurer’s price to the overall price distribution in a state and determine in which quartile each price falls. We then calculate the fraction of plans that belong to each quartile for each insurer in a given state. If price variation primarily reflects product differentiation at the firm level, insurers are likely to consistently set premiums in the same quartile for all the plans that they offer in a state. We find that this happens to on average 30 percent of insurers in a state. The remaining insurers on average have an equal number of plans in each of the four quartiles.24 If we compare each plan to the median of the price distribution, we find that on average 60 percent of insurers in a state charge prices for all offered plans consistently below or above the median. The remaining insurers tend to switch prices back and forth between below and above the median of the corresponding price distribution. Although these findings suggest that product differentiation is important, it alone cannot explain all the variation in premiums observed 23 Weiss Ratings rates each insurer as follows.“A” means the company offers excellent financial security; “B” means the company offers good financial security and has the resources to deal with a variety of adverse economic conditions; “C” means the company is currently stable, although during an economic downturn or other financial pressures it may encounter difficulties in maintaining its financial stability. A company is unrated for reasons such as total assets being less than $1 million or a lack of the information necessary to reliably issue a rating. 24 To be more specific, we find the proportion of plans belonging to each quartile averages 22 percent for the first quartile, 28 percent for the second, 29 percent for the third, and 21 percent for the fourth.

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in the data. To further examine the role of firm heterogeneity in explaining observed price variation, we follow an approach suggested by Sorensen (2000). We compare the R-squared of a regression of premiums on plan dummies, rating methods, and state dummies (column 1 of Table 3) to the R-squared of a similar specification that also includes insurer-fixed effects (column 3 of Table 3). Adding the insurer-fixed effects increases the R-squared from 0.39 to 0.68, accounting for about 48 percent of the variation unexplained by the regression if we leave out the insurer-fixed effects.25 We find similar results if we add the average claim as an explanatory variable (compare column 4 of Table 3 to column 2). We also conducted a regression with additional controls for state-insurer fixed effects; this increases the R-squared from 0.68 to 0.83, accounting for about 45 percent of the variation unexplained by the regression using only insurer-fixed effects. These results confirm that although a significant amount of variation in premiums can be absorbed by firm heterogeneity, product differentiation alone does not fully explain price variation across insurers within a state. Search An additional explanation for the observed price differences relates to search frictions.26 Given the large number of insurers in each market, it will be costly for consumers to obtain information on the plans and corresponding rates offered by each insurer. Since Medigap is supplemental insurance sold and administered by private insurers, no free and universal pricing information is available to consumers. The most comprehensive guide to choosing a Medigap policy is published annually by the Center of Medicare and Medicaid Services (CMS). The CMS suggests Medicare beneficiaries take the following three steps to acquire information about Medigap plans before subscribing to a plan: (1) decide which plan type to purchase; (2) find out which insurers are selling this plan type; and (3) call these insurers and compare costs. For step 2 the CMS advises beneficiaries to call the State Health Insurance Assistance Program or the State Insurance Department, or to visit medicare.gov. Note that these sources only provide a list of insurers that sell Medigap plans by state, which means that no pricing information is readily available. The CMS’s suggestion to call 25 Note that this comparison with and without controlling for firm fixed effects might lead us to overstate the importance of firm heterogeneity, because some price dispersion unrelated to firm differences will nevertheless be absorbed by the inclusion of fixed effects (Sorensen, 2000). 26 We study how search friction and product differentiation translate into price dispersion in identical Medigap plans. We do not specifically consider whether firms raise prices on existing enrollees after they are locked in (see, e.g., Ericson, 2014). Note that Ericson (2014) finds that firms introduce new and cheaper plans to attract new enrollees in Medicare Part D, which is prohibited in Medigap due to plan standardization. However, consumer inertia might exist in the Medigap market and it is possible that firms set prices low to attract consumer when they make their initial purchase decisions (typically when they turn to age 65 and enroll in Medicare Part B). This is interesting to explore but beyond the scope of this paper.

14

insurers to compare costs (step 3) can therefore be quite time consuming, especially given the large number of insurers in each state. The presence of several websites that facilitate search further supports the notion that search frictions play an important role in this market. For instance, Weiss Ratings has a comprehensive nationwide Medigap pricing information database. Weiss Ratings sells this information to consumers; currently the cost of acquiring information about all Medigap plans sold in a specific zip code is $99. Log(price) 8.2 8.0 7.8 7.6 7.4 7.2 7.0

-12

-10

-8

-6

-4

Log(market share)

Figure 1: Log price versus log market share (Plan G, Indiana) As shown by a large theoretical literature on consumer search, search frictions may lead to price dispersion in homogenous product markets (Burdett and Judd, 1983; Stahl, 1989) as well as markets for differentiated products (Anderson and Renault, 1999; Wolinsky, 1986). The results presented in the previous subsection suggest that firm differentiation is important in the Medigap market, so search frictions are unlikely to be only explanation for the price variation we observe in the data, ruling out a search model in which consumers search for homogenous products.27 Additional evidence that rules out search as the sole determinant of price dispersion derives from the relationship between market shares and prices. Were search to be the only explanation for price differences across insurers, one would expect to see a negative and monotonic relationship 27 In a typical homogenous good search model, the pricing equilibrium is in mixed strategies (see, for instance, Burdett and Judd, 1983; Stahl, 1989). We do not find evidence that supports mixed strategies in prices in the data. For instance, using three years of pricing data from 2007, 2008, and 2009, we find that more than 60 percent of insurers consistently set Medigap Plan F prices in the same quartile of the price distribution, and that more than 85 percent stuck to prices that were either below or above the median price. Moreover, around 10 percent of insurers charged the same prices between 2007 and 2009, and 30 percent had only one change in prices during the three-year period.

15

between price and market share (Horta¸csu and Syverson, 2004). In general, this is not the case in our data. For example, Figure 1 shows how market shares relate to prices for Medigap Plan G in Indiana—although there seems to be a weak negative relationship between the log price and log market share, this relationship is not monotonic. The insurer with the largest market share has the twelfth highest price out of 26 firms that offer plan G, and the insurer with the third largest market share has the fifth highest price. This lack of a monotonic relationship between price and market share also exists if we look at the market share of insurers, regardless of plan type.28 For example, in Indiana the insurer with the largest market share charges the fourth highest price; and the top five insurers in terms of market share all charge prices above the median of the overall price distribution. Since both the institutional details of the market and the data suggest that both search and product differentiation play a role in explaining observed price variation across insurers, in the next section we take search and product differentiation as our main ingredients for our theoretical and empirical framework. As in Anderson and Renault (1999) and Wolinsky (1986), our model also allows for horizontal product differentiation in order to capture uncertainty about which of the plans offered by an insurer most suits an individual. This means that in our model individuals are searching to find out price information as well as to figure out which of the Medigap plans offered by the insurers is the best match.

4

Model

4.1

Consumer Demand

Let the utility of consumer i for plan j ∈ {1, 2, . . . , J} sold by insurer f ∈ {1, 2, . . . , F } be given by uijf = x0jf β − αpjf + ξjf + εijf = δjf + εijf , where xjf are characteristics observed by both the researcher and the consumer, ξjf is a vertical characteristic observed by the consumer only, and εijf is a matching term unobserved by both the researcher and the consumer. The mean utility of product j sold by insurer f is given by δjf . The utility of not buying any of the plans is ui0 = εi0 . 28

An insurer’s market share is calculated by summing up market share for all plans offered by an insurer in a given state, whereas price is the average price across the plan offered.

16

We assume that consumers are searching nonsequentially for information about the plans. Consumers have information about xjf and ξjf , but not matching parameters εijf and prices pjf , so they search to discover these parameters. Search costs are randomly distributed in [0, ∞) according to the cumulative distribution function (CDF) G(c). We assume that ε follows a type I extreme −ε

value distribution with location parameter 0 and scale parameter 1, i.e., F (ε) = e−e . Let us start by examining consumers’ behavior. Since consumers do not know the realization of εijf and pjf before they start searching, they rank insurance companies according to their mean utility φf , where φf is the expected maximum utility of the set of plan types Gf on offer by firm P  29,30 f , i.e., φf = log j∈Gf exp[δjf ] . Note that this ranking is the same for all consumers, so we can index insurers by their ex-ante attractiveness, i.e, insurer f = 1 is the most attractive insurer, insurer f = 2 the second-most attractive, and so on. We assume consumers can only evaluate the value of the outside good after having searched, i.e., consumers do not observe εi0 before searching (so they will not condition their search behavior on this). Furthermore, we assume that the first observation is free, so that all consumers will search at least once. An individual consumer with search cost c chooses the number of insurance companies to sample, denoted k ∗ (c), to maximize her expected utility. That is, k ∗ (c) = arg max{E[max{uij1 , uij2 , . . . , uijk }] − (k − 1)c}, k

where (k − 1) reflects that the first observation is obtained for free. As shown by Moraga-Gonz´ alez, S´andor, and Wildenbeest (2015), assuming that εijf follows a type I extreme value distribution 29

Since εijf follows a type I extreme value distribution with location parameter 0 and scale parameter 1, we get     Z ∞ d Y F (u − δjf ) du; δf = E max {uijf } = u j∈Gf −∞ du j∈Gf   Z d Y exp [− exp [−(u − δjf )]] du; = u du j∈G f   X = log  exp[δjf ] . j∈Gf

Note that we have left out the Euler constant from δf , since it is common to all firms and therefore does not affect choices. 30 We use the standard assumption in the theoretical literature on search for differentiated products that consumers form rational expectations about prices (as in Wolinsky, 1986; Anderson and Renault, 1999). This means that even though consumers do not observe realized prices before searching, they use expected (equilibrium) prices to rank the firms.

17

allows us to write the optimal number of quotes to obtain as     k   X ∗   k (c) = arg max log 1 + exp φf − (k − 1)c .  k  f =1

We define c1 as the consumer who is indifferent regarding whether to obtain quotes from one insurer or from two insurers, i.e., ln(1 + eφ1 ) = ln(1 + eφ1 + eφ2 ) − c1 . Solving for c1 gives  c1 = ln 1 +

e φ2 1 + e φ1

 .

More generally, we define ck as the consumer who is indifferent regarding whether to search k or k + 1 times, i.e.,  ln 1 +

k X





eφf  − (k − 1)ck = ln 1 +

f =1

k+1 X

 eφf  − kck .

f =1

Solving for ck gives ck = ln 1 +

1+

eφk+1 Pk

φf f =1 e

! .

(1)

Note that by definition φk is decreasing in k, which means that ck is decreasing in k as well. Moreover, the above equation shows that critical search cost values cannot be negative. Using the critical search cost values ck and the search cost distribution G(c) we can calculate the fraction of individuals searching k times. The fraction of individuals searching once is µ1 = 1 − G(c1 ).

(2)

The fraction of individuals searching k ≥ 2 times is µk = G(ck−1 ) − G(ck ), k = 2, . . . , N − 1;

(3)

µN

(4)

= G(cN −1 ).

We now move to the discussion of aggregate demand. First consider plan j sold by the highestranked insurer (i.e., the firm with the highest mean utility φf ). Since all consumers will visit this

18

insurer, the market share of plan j is given by N

sj1 =

X eδj1 eδj1 eδj1 eδj1 · µ = · µ + · µ + . . . + · µk . P P P 1 2 N φ` 1 + e φ1 1 + 2`=1 eφ` 1+ N 1 + k`=1 eφ` `=1 e k=1

The second-highest-ranked insurance company will only attract the consumers who search at least twice, so the market share of a plan j sold by this insurer is

sj2 =

N X

eδj2 Pk

· µk .

φ` `=1 e

1+ k=2

More generally, the market share of a plan j sold by the f th-highest-ranked insurer is

sjf =

N X k=f

1+

eδjf Pk

`=1 e

· µk ,

φ`

while the overall market share of the f th-highest-ranked insurer is

sf =

N X k=f

1+

eφf Pk

φ`

1 Pk

φ`

`=1 e

· µk .

Using the market share of the outside good, i.e.,

s0 =

N X k=1

1+

`=1 e

· µk ,

we can rewrite sj1 as sj1 = s0 · eδj1 ,

(5)

or, by taking logs and rearranging, ln sj1 − ln s0 = δj1 . Similarly, again using the definition of s0 we can rewrite sj2 as  sj2 =

µ1 s0 − 1 + e φ1



· eδj2 .

Using s0 , the overall market share of the highest-ranked insurance company is s1 = s0 · eφ1 ,

19

(6)

which can be rewritten as 1 + eφ1 =

s0 + s1 , s0

which can be plugged into equation (6) to get sj2

 = s0 1 −

µ1 s0 + s1



· eδj2 .

Taking logs and rearranging gives 

µ1 ln sj2 − ln s0 = δj2 + ln 1 − s0 + s1

 .

Similarly, the market share equation for a plan sold by the third-highest-ranked insurer is ln sj3 − ln s0

   µ2 µ1 = δj3 + ln 1 − 1− . s0 + s1 s0 + s1 + s2 − µ1     µ1 µ2 = δj3 + ln 1 − + ln 1 − . s0 + s1 s0 + s1 + s2 − µ1

More generally, the difference between the log market share of plan j sold by the f th-highest-ranked insurance company and the log market share of the outside good can be written as

ln sjf − ln s0 = δjf +

f −1 X

ln 1 −

k=1

4.2

!

µk s0 +

Pk

`=1 s`

−

Pk

`=2 µ`−1

.

(7)

Estimation

We use equation (7) to estimate the model in the following way: ln sjf − ln s0 = βXjf − αpj + γ1 Rf 1 + γ2 Rf 2 + . . . + γN −1 Rf N −1 + ξj , where Rf k is a firm ranking-related dummy that is given by

Rf k

  1 if rank > k; f =  0 if rank ≤ k. f

Comparing equation (7) to equation (8) yields

γk = ln 1 − µk / s0 +

k X `=1

20

s` −

k X `=2

!! µ`−1

,

(8)

which means the estimated γk ’s can be used to back out the µk ’s, which represent the shares of consumers searching k times. Specifically, solving for µk gives

µk = [1 − exp(γk )] s0 +

k X `=1

s` −

k X

! µ`−1

.

`=2

The µk ’s can be obtained iteratively by starting with µ1 : to calculate µ1 only γ1 , s0 , and s1 are needed; to calculate µ2 , we can use the estimate of µ1 , as well as γ2 , s0 , s1 , and s2 . To derive a non-parametric estimate of the search cost distribution, we combine the estimates of the µk ’s with estimates of the search cost cutoffs ck . For this we can use equation (1) as well as estimates of the firm-specific logit inclusive value φf . The µk ’s can then be mapped into the quantiles of the search cost distribution that correspond to the search cost cutoff values by inverting equations (2)-(4). Note that φ2 cannot be larger than φ1 , so the minimum value of ln(1−µ1 /(s0 +s1 )) is ln s2 −ln s1 , while the maximum value is 0. Similarly, the minimum value of ln(1 − µ2 /(s0 + s1 + s2 − µ1 )) is ln s3 − ln s2 , while the maximum value is again 0. This means that we have to estimate equation (8) using the constraint that γk ∈ [ln sk+1 − ln sk , 0]. In defining the relevant market, we exclude individuals that would gain access to supplemental insurance through other sources such as employers and Medicaid.31 Our goal is to study search behavior and the decision to purchase Medigap insurance. This exclusion allows us to focus our study on people who would have to pay more than a nominal premium to obtain Medigap coverage. We estimate equation (8) using constrained two-stage least squares. In order to correct for the potential endogeneity of prices, we construct two instrumental variables in the spirit of Hausman (1996) and Nevo (2000). The first instrument is the average price of the same plan offered by the insurer in other states. The second is the average price of all plans offered by the insurer in other states. Note that the ranking-related dummies are market and firm specific. In carrying out our estimation, we pool firms ranked below a certain threshold altogether for the purpose of restricting the total number of these dummies. For example, in our main specification, we estimate a model in which one can either search any number from one to four, or they search five or more than five times, which allows them to obtain information on all the firms in the market. Our estimation imposes an implicit assumption that consumers either have relatively high search costs, such that they explicitly decide how many firms to search (up to five), or that they have search costs relatively low, such that they obtain all the information. Our results are robust to using a different cutoff, 31

Approximately 30 percent of those eligible for Medicare have access to employer sponsored supplemental coverage and about 14 percent through Medicaid.

21

such as six or seven searches.

4.3

Identification

In this section we discuss identification of the parameters of the utility function, which are given by α and β, as well as the parameters that reflect the search part of the model, which are given by the vector of ranking-related parameters γ. Variation in product and insurer characteristics together with variation in market share allows us to identify the α and β parameters of the utility function. Variation in market share that cannot be attributed to product and insurer characteristics allows us to identify γ. To better explain how search costs parameters γ are separately identified, let us consider two similar plans sold by two different firms, with one firm being slightly more desirable than the other.32 In a full information model, these two plans should have very similar market shares. However, in a search model, the more desirable firm will be ranked higher and therefore visited by more consumers, which gives the plan offered by this firm an additional boost in market share. As a result, differences in market share of similar products offered by firms that share similar attributes would allow us to identify the search costs parameters γ. As search costs increase, the market share of the plan offered by the more popular firm will increase relative to the plan offered by the less popular firm. The discussion above assumes we use insurer characteristics to capture firm heterogeneity. If we allow for firm fixed effects instead, separately identifying the effects of product differentiation from the search model is more challenging. It is worthwhile to note that the vector of search cost parameters γ varies across markets. Therefore, separately identifying firm fixed effects from search cost parameters requires observing multiple firms that share the “same” ranking in a given market. More specifically, identification can be achieved in the following two ways. First, firm fixed effects can be identified using variation in identities of the highest ranked firms across markets (and time). Identification works here by taking advantage of the fact that the highest ranked firm is part of all choice sets, so by construction no ranking-related dummies are needed for the highest ranked firms. Second, we assume that consumers search up to five firms, or search all firms. As a result, there will be multiple firms sharing the same “ranking” among firms ranked five or below, which allows us to separately identify firm fixed effects from the effect of the search-related ranking dummies. 32 Note that in our model consumers might value one firm more than the other even if the attributes of the firms are similar. For example, one firm could offer more product choices, which leads to a higher logit inclusive value for that firm and therefore a higher expected mean utility.

22

5

Results

5.1

Search Model

Table 4 reports the estimation results for the search model. In our main specification, presented in column 1 of the table, we estimate equation (8) by constrained two-stage least-squares. The price coefficient is negative and highly significant. Since search cost parameters γ vary across markets, we report these parameters by calculating their average across states. These coefficients indicate that the lower the ranking of a given firm, the smaller the market share of its products. Our main specification also controls for a set of insurer-related characteristics, such as financial safety rating, age of a firm, the number of different policies an insurer offers, the number of states in which an insurer is active, and whether the state is the insurer’s domicile. The estimates for the financial ratings indicate that firms with the best safety rating (rating “A”, the omitted group) are the most preferred and that firms with no rating are the least preferred. The coefficient on firms with a “D” rating is imprecisely estimated, due to the fact that only 3.5% of the firms fall into this category. Insurer age has a positive marginal utility, which is likely to reflect the reputation or stability of an insurer. The estimates for the indicator variables related to the number of states in which an insurer is active suggest that consumers prefer insurers that are active in less than 24 states, which suggests that consumers prefer local insurers. Consistent with this finding, we find a positive and highly significant parameter on the dummy variable for domicile state. Consumers also prefer insurers that offer multiple Medigap plans, as indicated by the positive and significant dummy variables related to the number of policies offered by the insurer. The estimated ratingmethod coefficients indicate that plans with an issued-age or community-rated rating method are more desirable than attained-age plans. This result suggests that policy holders value a rating method that offers some sort of protection against increases in premiums as they get older. All plan dummies have a positive coefficient and are highly significant, suggesting that all plans have a higher marginal utility than the omitted plan (Plan A, which is the basic plan and offers the least coverage of all plans). Not surprisingly, Plan J, the most comprehensive plan, has the highest marginal utility; and Plan F, the second-most comprehensive plan, has the second-highest marginal utility. Plan K has the lowest coefficient estimate of all plans included in the table, due to a higher out-of-pocket limit. Specification (1) is estimated using constrained two-stage least squares, where we use constraints on the ranking-related coefficients to make sure that the observed ranking of firms in terms of market share are consistent with the underlying search model. In specification (2) of Table 4 we relax those

23

Table 4: Estimation Results Search Model Variable Price

Coeff. -1.732

(1) Std. Err. (0.086)∗∗∗

Coeff.

(2) Std. Err.

-1.679

(0.093)∗∗∗

-0.739 -0.489 -0.397 -1.280

(0.165)∗∗∗ (0.160)∗∗∗ (0.157)∗∗ (0.114)∗∗∗

Ranking-related dummies (average) Ranked 2 or higher Ranked 3 or higher Ranked 4 or higher Ranked 5 or higher

-0.732 -0.664 -0.476 -0.321

Insurer characteristics Firm Weiss safety rating B Firm Weiss safety rating C Firm Weiss safety rating D No Weiss safety rating Age Number of states active 24 − 36 Number of states active > 36 Number of policies offered 4 − 7 Number of policies offered > 7 Domicile state

-0.191 -0.257 0.059 -0.491 0.002 -0.292 -0.086 0.261 0.255 0.531

(0.081)∗∗ (0.085)∗∗∗ (0.137) (0.108)∗∗∗ (0.001)∗∗ (0.072)∗∗∗ (0.081) (0.077)∗∗∗ (0.094)∗∗∗ (0.097)∗∗∗

-0.183 -0.171 0.171 -0.463 0.002 -0.169 0.054 0.163 0.170 0.465

(0.080)∗∗ (0.084)∗∗ (0.135) (0.106)∗∗∗ (0.001)∗∗ (0.072)∗∗ (0.080) (0.076)∗∗ (0.093)∗ (0.098)∗∗∗

Rating method Issued-age Community-rated

0.397 1.689

(0.092)∗∗∗ (0.297)∗∗∗

0.444 1.643

(0.091)∗∗∗ (0.293)∗∗∗

Plan dummies Plan B Plan C Plan D Plan E Plan F Plan G Plan H Plan I Plan J Plan K Plan L

0.862 2.119 1.853 1.398 4.073 2.496 2.102 2.455 4.531 0.452 0.689

(0.112)∗∗∗ (0.114)∗∗∗ (0.102)∗∗∗ (0.146)∗∗∗ (0.105)∗∗∗ (0.103)∗∗∗ (0.181)∗∗∗ (0.175)∗∗∗ (0.135)∗∗∗ (0.195)∗∗ (0.178)∗∗∗

0.861 2.133 1.867 1.387 4.087 2.496 2.093 2.445 4.519 0.502 0.753

(0.111)∗∗∗ (0.114)∗∗∗ (0.101)∗∗∗ (0.143)∗∗∗ (0.106)∗∗∗ (0.102)∗∗∗ (0.178)∗∗∗ (0.172)∗∗∗ (0.134)∗∗∗ (0.192)∗∗∗ (0.175)∗∗∗

Number of Observations R2 State Fixed Effects Firm Fixed Effects Plan Fixed Effects State-specific ranking-related dummies

4,704 0.529 yes no yes yes

4,704 0.542 yes no yes no

All specifications include a constant. ∗∗∗ Significant at the 1 percent level. at the 5 percent level. ∗ Significant at the 10 percent level.

24

∗∗

Significant

constraints and force the ranking-related coefficients to be the same across states. Notice that the ranking-related coefficients can be interpreted as the marginal effect of moving down the ranking. However, if we restrict these coefficients to be the same across states, there is no guarantee that the estimated ranking-related coefficients are consistent with the observed ranking of the firms in terms of market share in each individual state. As a result, we are unable to use these estimates to derive the search cost distribution. Apart from this, the parameter estimates are very similar to those reported in column 1 of Table 4. Not surprisingly, the fit, as measured by the R-squared, goes up. The release of the restrictions on the ranking-related parameters used for estimating specification (1) has the biggest effect on those firms that are ranked fifth or higher, since that parameter more than quadruples. In addition, the parameters on some of the insurer characteristics change in magnitude, but most other parameters do not change that much. Figure 2 provides the estimated search cost cumulative distribution function, averaged across states, for specification (1).33 Median search costs are approximately $30. According to the average search cost distribution, the 25th, 75th, and 90th percentiles are $13, $54, and $151, respectively. On average, 39 percent of consumers searches once, 22 percent searches twice, 14 percent searches three times, 6 percent searches four times, and 19 percent of consumers searches five or more times. G(c) 1.0

0.8

0.6

0.4

0.2

0.0

0

50

100

150

200

c (in $)

Figure 2: Estimated search costs (averaged across states) 33 For each state we get non-parametric estimates of the search cost distribution. We the obtain the curves in Figure 2 by fitting a log-normal distribution through the estimated points on the search cost CDF of each state and then taking the average fitted CDF across states.

25

5.2

Comparison to Alternative Models

Insurer Fixed Effects To capture heterogeneity across insurers, we use a relatively rich set of controls in our main specification and argue that these controls explain a good amount of heterogeneity across firms. However, it might be possible that part of the insurer-level heterogeneity that affects the decision making of consumers is unobserved by the researcher. To see to what extent our estimates would change if we control for unobserved heterogeneity at the firm level, in column 1 of Table 5 we drop the insurerspecific covariates and include insurer fixed effects instead. As discussed in Section 4.3, to be able to separately identify firm fixed effects from the ranking-related parameters, we exploit variation in firm identities that share the “same” ranking across markets. In conducting this analysis, we add an additional year of data (2010) to our original data. To be able to make a fair comparison between this model and the model that does not include firm fixed effects, we re-estimate the original model using both 2009 and 2010 data. G(c) 1.0

0.8 firm fixed effects (2009/2010)

0.6

no firm fixed effects (2009/10) 0.4

no firm fixed effects (2009)

0.2

0.0

0

50

100

150

200

c (in $)

Figure 3: Estimated search costs (firm fixed effects) As can be seen from comparing columns 1 and 2 of Table 5, most parameter estimates are very similar. The only parameters that are further apart are the estimated rating method parameters— in the model without insurer fixed effects the coefficient on community rating is much larger than the coefficient on issue-age rating. The estimated price coefficients as well as the average rankingrelated coefficients, however, are very similar. As a result there is not much difference in estimated search costs, as can also be seen from Figure 3. In this graph the solid black curve represents the search cost CDF when using firm fixed effects, while the search cost CDF for the model without fixed effects is shown by the dashed black curve. Also plotted is the search cost CDF obtained when

26

Table 5: Estimation Results Insurer Fixed Effects Variable Price Ranking-related dummies (average) Ranked 2 or higher Ranked 3 or higher Ranked 4 or higher

Coeff. -1.558

(1) Std. Err. (0.089)∗∗∗

-0.539 -0.520 -0.457

(2) Std. Err.

-1.578

(0.065)∗∗∗

-0.614 -0.668 -0.547

Insurer characteristics Firm Weiss safety rating B Firm Weiss safety rating C Firm Weiss safety rating D No Weiss safety rating Age Number of states active 24 − 36 Number of states active > 36 Number of policies offered 4 − 7 Number of policies offered > 7 Domicile state Rating method Issued-age Community-rated

Coeff.

-0.257 -0.293 -0.118 -0.653 0.003 -0.110 0.061 0.374 0.379 0.697

(0.061)∗∗∗ (0.065)∗∗∗ (0.087) (0.087)∗∗∗ (0.001)∗∗∗ (0.056)∗∗ (0.062) (0.057)∗∗∗ (0.067)∗∗∗ (0.077)∗∗∗

0.691 0.702

(0.091)∗∗∗ (0.209)∗∗∗

0.259 2.051

(0.077)∗∗∗ (0.197)∗∗∗

Plan dummies Plan B Plan C Plan D Plan E Plan F Plan G Plan H Plan I Plan J Plan K Plan L Plan M Plan N

0.794 1.985 2.034 1.752 4.291 2.581 2.721 2.661 4.908 -0.263 0.331 -2.386 1.617

(0.080)∗∗∗ (0.087)∗∗∗ (0.079)∗∗∗ (0.130)∗∗∗ (0.082)∗∗∗ (0.074)∗∗∗ (0.163)∗∗∗ (0.157)∗∗∗ (0.120)∗∗∗ (0.121)∗∗ (0.112)∗∗∗ (0.219)∗∗∗ (0.094)∗∗∗

0.728 1.913 1.570 1.261 3.974 2.282 1.861 2.267 4.332 0.216 0.566 -1.925 1.366

(0.086)∗∗∗ (0.085)∗∗∗ (0.081)∗∗∗ (0.140)∗∗∗ (0.076)∗∗∗ (0.075)∗∗∗ (0.176)∗∗∗ (0.170)∗∗∗ (0.125)∗∗∗ (0.123)∗ (0.121)∗∗∗ (0.238)∗∗∗ (0.104)∗∗∗

Year dummies 2010

0.182

(0.038)∗∗∗

0.321

(0.040)∗∗∗

Number of Observations R2 State Fixed Effects Firm Fixed Effects Plan Fixed Effects State-specific ranking-related dummies

8,601 0.614 yes yes yes yes

8,601 0.516 yes no yes yes

All specifications include a constant. ∗∗∗ Significant at the 1 percent level. ∗∗ Significant at the 5 percent level. ∗ Significant at the 10 percent level. We use three ranking-related dummies in both specifications because in 2010 there is one state in which only four firms are active.

27

using just the 2009 data and no firm fixed effects, as in the main specification. Median search costs are smaller in the model with firm fixed effects, which is as expected, since part of the variation in market shares that is attributed to search frictions in our main specification is picked up by the insurer-fixed effects as unobserved heterogeneity. Unfortunately there is no good way of knowing whether the observed variation in market shares is due to unobserved insurer heterogeneity or such variation should be attributed to the ranking-related effects caused by search frictions. However, because of the relatively rich set of firm-level controls we use in our main specification and the fact that we find largely similar results even if we control for firm fixed effects, we are confident that a significant part of the variation in market shares that remains after controlling for observed firm heterogeneity can be attributed to the search model. Alternative Rankings Column 1 of Table 6 gives estimation results for a specification in which we do not impose any constraints on ranking-related parameters in equation (8). These constraints imposed in our search model make the ranking of firms endogenous: consumers form rational expectations of the utility of each firm and search higher valued firms first. A model without imposing these constraints can be interpreted as a model with an exogenous ordering of firms according to decreasing market share. Note that these parameters are still allowed to vary across markets. The estimation results are very close to the main specification, suggesting that those constraints cannot be rejected in the data. The fit of the model, as measured by the R-squared, increases. Regarding the ordering of firm, it is possible that due to word-of-mouth effect, firms with a larger market share in previous years are more likely to become part of consumers’ choice sets. Column 2 gives estimation results for a specification that uses an exogenous ordering based on market shares in previous years. More specifically, we use the ranking of firms according to the number of current policies (active in 2009) that were sold before 2007, and use this as the order of search for our estimation. The estimated price coefficient is similar to that of our main specification. In column 3 of Table 6 we estimate the model assuming consumers visit firms alphabetically, by firm names. Moreover, the ranking-related parameters (averaged across states) are either positive, or no longer significantly different from zero, which suggests consumers are not very likely to search firms alphabetically. The price coefficient is also very similar to the full information case (see the last column of Table 6), which gives another indication that this particular ranking of firms does not add much in comparison to the model that assumes consumers have full information. As indicated by the lower R-squared, the model also gives a worse fit than the search model. 28

Table 6: Estimation Results Alternative Specifications

Variable

Coeff.

(1) Std. Err.

Alternative Rankings (2) Coeff. Std. Err.

Coeff.

(3) Std. Err.

-1.805

(0.096)∗∗∗

-1.796

(0.093)∗∗∗

-2.079

(0.101)∗∗∗

Ranking-related dummies (average) Ranked 2 or higher Ranked 3 or higher Ranked 4 or higher Ranked 5 or higher

-0.774 -0.524 -0.495 -1.275

(0.173)∗∗∗ (0.170)∗∗∗ (0.171)∗∗∗ (0.130)∗∗∗

-0.927 -0.443 -0.399 -1.434

(0.182)∗∗∗ (0.175)∗∗ (0.174)∗∗ (0.132)∗∗∗

0.827 -0.390 -0.097 0.344

(0.229)∗∗∗ (0.239) (0.251) (0.190)∗

Insurer characteristics Firm Weiss safety rating B Firm Weiss safety rating C Firm Weiss safety rating D No Weiss safety rating Age Number of states active 24 − 36 Number of states active > 36 Number of policies offered 4 − 7 Number of policies offered > 7 Domicile state

-0.151 -0.040 0.225 -0.422 0.003 0.008 0.263 0.274 0.245 0.175

(0.090)∗ (0.092) (0.138) (0.113)∗∗∗ (0.001)∗∗∗ (0.080) (0.091)∗∗∗ (0.080)∗∗∗ (0.097)∗∗ (0.117)

-0.107 0.049 0.288 -0.237 0.003 -0.052 0.129 0.409 0.219 0.020

(0.092) (0.093) (0.137)∗∗ (0.114)∗∗ (0.001)∗∗ (0.078) (0.090) (0.081)∗∗∗ (0.100)∗∗ (0.120)

-0.069 -0.310 -0.044 -0.854 0.008 -0.530 -0.297 0.453 0.450 0.760

Rating method Issued-age Community-rated

0.423 1.714

(0.093)∗∗∗ (0.353)∗∗∗

0.345 1.423

(0.094)∗∗∗ (0.405)∗∗∗

Plan dummies Plan B Plan C Plan D Plan E Plan F Plan G Plan H Plan I Plan J Plan K Plan L

0.887 2.205 1.915 1.401 4.186 2.576 2.105 2.469 4.600 0.361 0.662

(0.109)∗∗∗ (0.113)∗∗∗ (0.100)∗∗∗ (0.142)∗∗∗ (0.107)∗∗∗ (0.101)∗∗∗ (0.175)∗∗∗ (0.170)∗∗∗ (0.133)∗∗∗ (0.191)∗ (0.172)∗∗∗

0.927 2.175 1.971 1.465 4.202 2.600 2.210 2.545 4.690 0.430 0.702

(0.109)∗∗∗ (0.113)∗∗∗ (0.100)∗∗∗ (0.142)∗∗∗ (0.106)∗∗∗ (0.101)∗∗∗ (0.175)∗∗∗ (0.170)∗∗∗ (0.132)∗∗∗ (0.190)∗∗∗ (0.173)∗∗∗

Number of Observations R2 State Fixed Effects Firm Fixed Effects Plan Fixed Effects State-specific ranking-related dummies

4,704 0.565 yes no yes yes

Price

29

All specifications include a constant. ∗ Significant at the 10 percent level.

∗∗∗

4,704 0.563 yes no yes yes

Significant at the 1 percent level.

-2.116

(0.098)∗∗∗

(0.091) (0.095)∗∗∗ (0.146) (0.123)∗∗∗ (0.001)∗∗∗ (0.081)∗∗∗ (0.092)∗∗∗ (0.086)∗∗∗ (0.110)∗∗∗ (0.111)∗∗∗

-0.065 -0.362 -0.007 -0.629 0.004 -0.521 -0.296 0.382 0.463 0.977

(0.088) (0.092)∗∗∗ (0.148) (0.116)∗∗∗ (0.001)∗∗∗ (0.078)∗∗∗ (0.088)∗∗∗ (0.083)∗∗∗ (0.101)∗∗∗ (0.105)∗∗∗

0.465 2.034

(0.103)∗∗∗ (0.314)∗∗∗

0.408 2.068

(0.100)∗∗∗ (0.321)∗∗∗

0.953 2.289 1.882 1.517 4.290 2.638 2.183 2.534 4.581 0.356 0.784

(0.119)∗∗∗ (0.123)∗∗∗ (0.109)∗∗∗ (0.154)∗∗∗ (0.115)∗∗∗ (0.109)∗∗∗ (0.190)∗∗∗ (0.186)∗∗∗ (0.147)∗∗∗ (0.206)∗ (0.187)∗∗∗

0.943 2.279 1.849 1.456 4.243 2.596 2.124 2.454 4.672 0.324 0.684

(0.122)∗∗∗ (0.125)∗∗∗ (0.111)∗∗∗ (0.158)∗∗∗ (0.117)∗∗∗ (0.112)∗∗∗ (0.196)∗∗∗ (0.190)∗∗∗ (0.147)∗∗∗ (0.211) (0.193)∗∗∗

4,704 0.488 yes no yes yes ∗∗

Full Information (4) Coeff. Std. Err.

Significant at the 5 percent level.

4,704 0.444 yes no yes yes

Full Information Most existing discrete choice models of demand assume that consumers have full information. To see to what extent our search model gives different estimates in comparison to a model that assumes full information, we estimate a standard conditional logit model of demand. Notice that the full information model is a special case of our search model; by setting all ranking-related coefficients in equation (8) to zero, we get the standard conditional logit model of demand. Column 4 of Table 6 gives estimates for the full information model, which we estimate by two-stage least squares. The estimated price coefficient is higher in absolute sense in comparison to the estimates for the search model, which indicates that assuming full information when individuals have limited information due to search frictions leads to an upward bias in the absolute value of the estimated price coefficient. Although we allow consumers in our model to differ in terms of search costs, they are assumed to be similar in terms of their utility parameters. Whether this is an important limitation of the model is an empirical question. Unfortunately, our data lacks a suitable search cost shifter, which is a necessary requirement for estimating a richer search model (see Moraga-Gonz´alez, S´andor, and Wildenbeest, 2015). Instead we have estimated a full information model that allows for heterogeneity in some of the preference parameters, to see if in such a setting this factor makes a substantial difference on the estimated parameters. Specifically, we have estimated a random coefficient logit model in which we control for price endogeneity in a similar way as in the search model (following Berry, Levinsohn, and Pakes, 1995; Nevo, 2000). We assume that the price coefficient follows a normal distribution and estimate its mean and standard deviation. The estimated standard deviation parameter is close to zero and very imprecisely estimated. As a result, the parameter estimates are virtually identical to the estimates in column 4 of Table 6 which suggests that allowing for heterogeneity in the price coefficient is not critical.

5.3

Price elasticities

Table 7 reports the estimated demand elasticities for Medigap Plan F for the top-five insurers in Indiana, ranked by decreasing market share, for both the search model and the full information model. The diagonal entries indicate that estimated demand is more inelastic in the search model than in the full information model. In both panels Mutual of Omaha, the insurer with the largest market share in Indiana, has the most inelastic demand for Medigap Plan F. However, while the percentage change in market share after a competitor’s price change is the same for all insurers in the full information model, in the search model individuals are more likely to switch to insurers that

30

Table 7: Demand Elasticities Plan F (Indiana) Omaha

Anthem

Royal Neighbors

Admiral Life

United Commercial

Search Mutual of Omaha Anthem Insurance Royal Neighbors Of America Admiral Life Insurance Company of America Order of United Commercial Travelers

-1.957 0.294 0.161 0.133 0.113

0.067 -2.685 0.164 0.136 0.115

0.006 0.028 -3.037 0.081 0.069

0.006 0.028 0.097 -2.244 0.099

0.003 0.015 0.053 0.063 -2.724

Full information Mutual of Omaha Anthem Insurance Royal Neighbors Of America Admiral Life Insurance Company of America Order of United Commercial Travelers

-2.429 0.440 0.440 0.440 0.440

0.100 -3.546 0.100 0.100 0.100

0.017 0.017 -3.812 0.017 0.017

0.020 0.020 0.020 -2.864 0.020

0.013 0.013 0.013 0.013 -3.404

Notes: Percentage change in market share of insurer i with a 1 percent change in the price of insurer j, where i indexes rows and j columns. Obtained using the estimates in Column 1 of Table 4 for the search model and Column 4 of Table 6 for the full information model.

are similarly ranked. This is intuitive: an individual subscribing to Order of United Commercial Travelers must have relatively low search costs, which means that she is likely to have the other insurers in her choice set, making it more likely that she will find a good deal at an insurer that is also relatively low ranked, such as Admiral Life Insurance Company of America. Similarly, Mutual of Omaha gets a more than proportional share of the high-search-cost individuals, which makes it less likely that many individuals will switch to one of the lower-ranked insurers in case of a price increase of Mutual of Omaha plans. Table 8 looks in more detail at substitution patterns among the plans provided by Anthem Insurance, the second-largest provider in Indiana. Note that although the cross-price elasticities are uniformly higher in the search model, as in the full information model a percentage increase in price leads to the same percentage increase in all plans’ market shares. The reason for this is that we assume a single search cost for getting information on all plans sold by an insurer, making searching less of an issue when substituting within an insurer.

5.4

Counterfactuals

Our model can be used to study what happens to prices and market shares as a result of changes in search costs.34 To proceed, we first model the supply side to obtain marginal cost estimates. 34

As in most of the existing literature on consumer demand, we do not allow firms to change the plans they offer.

31

Table 8: Demand Elasticities Anthem Insurance (Indiana) Plan A

Plan B

Plan C

Plan D

Plan E

Plan F

Plan G

A B C D E F G

-2.070 0.032 0.032 0.032 0.032 0.032 0.032

0.001 -2.803 0.001 0.001 0.001 0.001 0.001

0.005 0.005 -2.852 0.005 0.005 0.005 0.005

0.001 0.001 0.001 -3.086 0.001 0.001 0.001

0.001 0.001 0.001 0.001 -2.973 0.001 0.001

0.300 0.300 0.300 0.300 0.300 -2.685 0.300

0.071 0.071 0.071 0.071 0.071 0.071 -2.533

Full information Plan A Plan B Plan C Plan D Plan E Plan F Plan G

-2.557 0.011 0.011 0.011 0.011 0.011 0.011

0.000 -3.425 0.000 0.000 0.000 0.000 0.000

0.002 0.002 -3.488 0.002 0.002 0.002 0.002

0.000 0.000 0.000 -3.771 0.000 0.000 0.000

0.000 0.000 0.000 0.000 -3.632 0.000 0.000

0.100 0.100 0.100 0.100 0.100 -3.546 0.100

0.024 0.024 0.024 0.024 0.024 0.024 -3.157

Search Plan Plan Plan Plan Plan Plan Plan

Notes: Percentage change in market share of plan i with a 1 percent change in the price of plan j, where i indexes rows and j columns. Obtained using the estimates in Column 1 of Table 4 for the search model and Column 4 of Table 6 for the full information model.

The profits of an insurer f supplying a subset Gf of J plan types are given by Πf =

X

(pr − mcr )M sr (p),

r∈Gf

where M is the number of consumers in the market. Assuming insurers set prices to maximize profits, the following first-order conditions should be satisfied: sj (p) +

X

(pr − mcr )

r∈Gf

∂sr (p) = 0. ∂pj

To obtain the marginal cost of each plan we solve for mc, i.e., mc = p − ∆(p)−1 s(p), where ∆ is a J by J matrix with the element in row j and column r given by

∆jr

   − ∂sr , if r and j are supplied by the same insurer; ∂pj =   0, otherwise.

32

(9)

For the derivation of the derivatives of the market shares with respect to prices we assume that consumers choose the insurers from which they will obtain quotes before they observe prices (see the Appendix). This means we use the standard assumption that consumers form rational expectations about prices but do not observe price deviations before searching (as in Wolinsky, 1986; Anderson and Renault, 1999). We obtain marginal cost estimates using equation (9) as well as the demand estimates from Table 4. Once we have obtained marginal cost estimates, we simulate to what extent prices would change if search cost is eliminated. We find that the average price decreases by the amount of $63, which corresponds to a change of 3.7 percent.35 Table 9: Change in Coefficient of Variation Observed prices

Plan Type A B C D E F G H I J K L

average price

max-min

coefficient of variation

1,128 1,567 1,804 1,437 1,509 1,813 1,422 1,468 1,515 1,746 1,030 1,456

869 959 1,490 927 535 1,889 868 278 319 721 215 322

0.173 0.181 0.173 0.131 0.110 0.196 0.155 0.049 0.071 0.102 0.079 0.079

Simulated prices (full information) average coefficient price max-min of variation 1,106 1,506 1,730 1,372 1,458 1,728 1,369 1,393 1,450 1,661 997 1,397

831 920 1,430 869 498 1,804 833 272 315 673 182 314

0.168 0.168 0.166 0.132 0.102 0.182 0.142 0.048 0.072 0.099 0.069 0.080

Notes: Obtained using estimates in Column 1 of Table 4. Plans only include those rated according to attained-age. The coefficient of variation is weighted by sales. Prices are in US$.

Table 9 summarizes changes in prices and price dispersion by plan type. A comparison of observed prices, which are used to estimate the model, to simulated prices shows that average prices decrease for all plans when moving to a full information equilibrium. Price dispersion also decreases, as measured by either the difference between the maximum and minimum price or the coefficient variation (weighted by market share of each plan),36 although the differences are small.37 Note that price dispersion is not expected to disappear in the case of zero search costs: due to product differentiation, firms with more favorable characteristics can set higher prices, which 35

The case of eliminating search costs can be interpreted as consumers being offered a price menu for all plans sold in a state at no cost. Currently no such information is made publicly available. Some aggregate data on premium ranges at the state-plan type level have become accessible through medicare.gov starting in 2012. 36 Using an unweighted coefficient of variation gives similar results, although the differences between observed and simulated prices are larger for unweighted measures. 37 The results in Table 9 are obtained using the estimates from Column 1 of Table 4.

33

results in price dispersion even in the case of full information. To analyze changes in consumer welfare we use compensating variation (see also Small and Rosen, 1981; Nevo, 2000), which in our search model corresponds to N P

CV =

k=1

µpost k

        k N k P P P pre post post pre pre − (k − 1)e ck exp φ` µk ln 1 + exp φ` − (k − 1)e ck − ln 1 + k=1

`=1

`=1

,

α (10)

where e ck is the average search cost of consumers searching k times. This amounts to the expected maximum utility when searching k times (measured in dollars by normalizing by the price coefficient), averaged over all k groups of consumers, taking average search costs for individuals in each group into account.38 The average change in consumer surplus when moving to the simulated zero search cost equilibrium is $236, which is close to four times the magnitude of the average price decrease ($63). Such changes in consumer welfare are driven by multiple factors such as savings on search costs, reduction in premiums, and expansion of the total market.

6

Conclusion and Discussion

In this paper we use market share and price data on Medigap plans to estimate the effect of search frictions on demand parameters. In our model consumers search among insurers for both the right plan type and prices. We have shown how to estimate the model using constrained two-stage least squares. Our estimates indicate that the search model provides a better fit than a model that assumes consumers have full information. Assuming full information when consumers in fact have limited choice sets leads to a higher estimated price coefficient in absolute sense. Moreover, search costs are found to be substantial: median search costs are estimated to be $30. Using the estimated parameters, we simulate equilibrium prices when search costs completely disappear. Depending on the exact specification, prices are expected to decreases by 3.7 percent, which corresponds to an average yearly savings of $63. If we take into account savings on the actual costs of searching and expansion of market shares due to lowered premiums, our findings are even more striking: average consumer welfare increases by $236 when moving to a zero-search-cost equilibrium. One of the main contributions of our paper is to provide a methodology that allows us to non-parametrically estimate search costs for differentiated goods when using aggregate data on consumer demand. Even though our paper primarily focuses on the market for Medigap insurance 38

For the case in which the new search costs are zero, we set µN = 1 while all other µk ’s are zero.

34

products, our model is general enough to be applied to other markets in which both search frictions and product differentiation coexist, and that lack suitable search cost shifters. One limitation of our paper is that we do not specifically model consumer selection into Mediap plans. Note that the existing literature has found mixed evidence of selection in Medigap plans (Fang, Keane, and Silverman, 2008).39 Moreover, allowing for both selection and search frictions is a huge challenge that is better addressed in future work. Nevertheless, we do offer some discussion on how our results would be affected if firms are able to take selection into account when setting prices. One obvious complication is that marginal costs may be related to prices, which leads to an additional channel through which prices affect profits.40 For example, an increase in price may scare away price-sensitive consumers, who may be more likely to have worse than average health conditions. In such a scenario marginal costs would be negatively related to prices, which means our current model is likely to overestimate marginal costs as well as the new equilibrium prices in the counterfactual of no search frictions. Moreover, if this would be the case, our counterfactual results should be considered as a lower bound with respect to price decreases.

39

Due to regulations in Medigap (such as product standardization and guarantee issues), we suspect that firms are limited in their capability to choose product characteristics and set prices. 40 In our model, marginal cost is kept constant but allowed to vary across firms and plans.

35

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Hortac ¸ su, A. and Syverson, C. “Product Differentiation, Search Costs, and Competition in the Mutual Fund Industry: a Case Study of S&P 500 Index Funds.” Quarterly Journal of Economics, Vol. 119 (2004), pp. 403–456. Hurd, M. and McGarry, K. “Medical Insurance and the Use of Health Care Services by the Elderly.” Journal of Health Economics, Vol. 16 (1997), pp. 129–154. Maestas, N., Schroeder, M., and Goldman, D. “Price Variation in Markets with Homogeneous Goods: The Case of Medigap.” Working Paper No. 14679, NBER, Cambridge, 2009. Robst, J. “Estimation of a Hedonic Pricing Model for Medigap Insurance.” Health Services Research, Vol. 41 (2006), pp. 2097–2113. ´ lez, J.L., Sa ´ ndor, Z., and Wildenbeest, M. “Consumer Search and Prices Moraga-Gonza in the Automobile Market.” Mimeo, 2012. Nevo, A. “Mergers with Differentiated Products: the Case of the Ready-to-Eat Cereal Industry.” RAND Journal of Economics, Vol. 31 (2000), pp. 395–421. Sheingold, S., Shartzer, A., and Ly, D. “Variation and Trends in Medigap Premiums.” ASPE Report, U.S. Department of Health and Human Services, 2011. Small, K. and Rosen, H. “Applied Welfare Economics with Discrete Choice Models.” Econometrica, Vol. 49 (1981) 105–130. Sorensen, A. “Equilibrium Price Dispersion in Retail Markets for Prescription Drugs.” Journal of Political Economy, Vol. 108 (2000), pp. 833–850. Stahl, D. “Oligopolistic Pricing with Sequential Consumer Search.” American Economic Review, Vol. 79 (1989), pp. 700–712. Starc, A. “Insurer Pricing and Consumer Welfare: Evidence from Medigap.” RAND Journal of Economics, Vol. 45 (2014), pp. 198–220. Stigler, G. “The Economics of Information.” Journal of Political Economy, Vol. 69 (1961), pp. 213–225. Weitzman, M. “Optimal Search for the Best Alternative.” Econometrica, Vol. 47 (1979), pp. 641–654.

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38

APPENDIX The derivative of the market share of insurer f ’s plan j with respect to its own price is given by ∂sjf ∂pjf

  Pk φ` − eδjf N eδjf 1 + e X `=1 · µk . = −α ·  2 Pk 1 + `=1 eφ` k=f

The derivative of the market share of insurer f ’s plan j with respect to the price of insurer f ’s plan g is N

X ∂sjf =α·  ∂pgf k=f

eδjf eδgf 2 · µ k . P 1 + k`=1 eφ`

The derivative of the market share of insurer f ’s plan j with respect to the price of insurer h’s plan g is ∂sjf =α· ∂pgh

N X

 k=max[f,h]

eδjf eδgh 2 · µ k . P 1 + k`=1 eφ`

39